Question

If an angle bisector in a triangle is its altitude, prove that the triangle is isosceles

Answer 1

Prove that a triangle AC is isosceles, if: (i) altitude AD bisects angle ∠ BAC, or (ii) bisector of angle BAC is perpendicular to base BC. Solution In ΔABC, let the altitude AD bisects ∠BAC. Then we have to prove that the ΔABC is isosceles.